Testing the distributional assumptions of least squares linear regression

The error terms in least squares linear regression are assumed to be normally distributed with equal variance (homoskedastic), and independent of one another. If any of these distributional assumptions are violated, several of the desirable properties of a least squares fit may not hold. A variety of statistical tests of the assumptions is available. The following are recommended for reasons of ease of use and discriminating power: the K2 test for testing for non-normality, either the Durbin-Watson test or the Q-test for testing for autocorrelation, and either Szroeter's or White's test for testing for heteroskedasticity. The assumptions should be tested in this order; violating one of the assumptions may invalidate the results of subsequent tests. A microcomputer-based software package for least squares linear regression that incorporates the above tests is introduced. Key words: normality, homoskedasticity, independence